To determine if you are getting enough jelly beans to make the trip to the specialty store worthwhile, we need to compare the total cost of buying jelly beans at both locations. We'll use two equations to represent the total costs at the specialty store and the supermarket.
Let's break down the costs:
1. Specialty Store:
- Jelly beans cost [tex]$\$[/tex] 1.30[tex]$ per pound.
- You spend $[/tex]\[tex]$ 3$[/tex] on gas each trip.
- The total cost [tex]\(C\)[/tex] at the specialty store can be represented as:
[tex]\[
C = 3.00 + 1.30x
\][/tex]
2. Supermarket:
- Jelly beans cost [tex]$\$[/tex] 2.10$ per pound.
- There is no additional cost like gas.
- The total cost [tex]\(C\)[/tex] at the supermarket can be represented as:
[tex]\[
C = 2.10x
\][/tex]
To find the break-even point where the total costs at both locations are equal, we set the two equations equal to each other:
[tex]\[
3.00 + 1.30x = 2.10x
\][/tex]
Now, let's check the given options with these two equations:
- Option a:
[tex]\[
\begin{array}{l}
C = 3.00 + 1.30x \\
C = 2.10x
\end{array}
\][/tex]
This matches our equations.
- Option b:
[tex]\[
\begin{array}{l}
C = 3.00 + 2.10x \\
C = 1.30x
\end{array}
\][/tex]
This does not match our equations.
- Option c:
[tex]\[
\begin{array}{l}
C = 2.10x + 1.30x \\
C = 3.00
\end{array}
\][/tex]
This does not match our equations.
- Option d:
[tex]\[
\begin{array}{l}
C = 3.10x \\
C = 3.00
\end{array}
\][/tex]
This does not match our equations.
So, the correct set of equations to determine the break-even point is given in option a:
[tex]\[
\begin{array}{l}
C = 3.00 + 1.30x \\
C = 2.10x
\end{array}
\][/tex]
